I can't even understand how a functioning human mind can think otherwise
Mihawk is like Zoro, someone who would die for his blade, he lives and breathes it. Mihawk loves his ''little'' sword Yoru so much.
But I highly doubt Shanks does the same thing with his sword Gryphon. It'd be boring if Shanks will just swing his sword and do nothing else like Mihawk and Zoro. But since Oda already put great emphasis on Shank's powerful haki, I think he might just make him fight differently too, and not make him focus just on his sword, but on other stuff as well. Maybe guns? It really depends on Oda's creativity here.